Easy questions first:
If you are PCSd here, you are functionally a California resident; your military ID will satisfy for gun purchases.
No, you may not buy guns online directly, either instate or interstate; they must go through a California-licensed FFL.
Now: the loaded firearm charge. I don't know for sure, but I think it's likely that the charge will show up when the state runs the background check.
Misdemeanor violation of PC 12031 is not on the
list that CA-DOJ publishes of crimes that create firearms disabilities. But 12031 can also be prosecuted as a felony. I don't think that's the case for your event, but you ought to know how you were booked.
If you really want to know your status, cheaply, and not get dinged for illegally attempting to get a firearm, download and file this form:
Personal Firearms Eligibility Check Application; it'll cost you $20 and a notary fee, and apparently isn't real high on their priority list
DOJ will make every effort to process PFECs within 30 days, however, please allow 90 - 120 days for the processing of your application. You will be notified via U.S. Mail.
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ETA -- since you go to court mid-month, don't you think it'd be wiser not to post in public gun forums for a bit? You might ask your lawyer...